Let’s say for example, that your aim is for David to keep his seat, and for challengers Nancy and Nicholas to be elected. With regard to the rest of the field, some of them are sort of okay but you are largely indifferent. In this case the best strategy is to vote only for David, Nancy, and Nicholas — even though you have the option of selecting three other individuals. If you choose more than three, you will pile up extra votes for mediocre candidates, and you may therefore prevent your favorite candidates from making it into the top six. In short, every vote for a mediocre candidate is a vote against the candidate whom you really want to see in office.
When would it make sense to use all six of your votes? Well, I suppose that would be reasonable if you believe that there are exactly six candidates who are all quite worthy and equal to one other; that there are none whom you would favor over others, and you would be regretful if any of your six should fail to be elected.
Another case would be when your only intent is to vote against a particular candidate. Say, for example, your only purpose is to finally dislodge Tom. In that case, you would want to vote against Tom by maximizing your votes against him and choosing six other “least worst” candidates. I hope that this would be a very rare case, however. Almost always it will make far more sense to identify those individuals whom you really want to see in office, and vote only for them.